### Function Festival Fall 2000

# Ashish Poonia, Math Artist

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My function is: Z = f(x,y) = (x^2/25)+(y^2/100)

and I have to find the directional derivatives

(grad Z.u, grad Z.v) from point A(3,3,0.45) to

points B(6,-3,1.53) and C(-6,3,1.53).

AB = 3i-6j, Unit vector in the direction of AB,

u = i/(5^.5)-2j/(5^.5)

AC = -9i , Unit vector in the direction of AC,

v = -i

Grad Z = (2x/25)i+(2y/100)j

and then

Grad Z at(3,3)=(6/25)i+(3/50)j

grad Z.u = [6/25)i+(3/50)j].[i/(5^.5)-2j/(5^.5)]

= 0.05366563146

grad Z.v=[6/25)i+(3/50)j].[-i]

= -0.24

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